Queueing Network Research Articles

Unleashing the Power of Paying Multiplexing Only Once in Stochastic Network Calculus

The stochastic network calculus (SNC) holds promise as a versatile and uniform framework to calculate probabilistic performance bounds in networks of queues. A great challenge to accurate bounds and efficient calculations are stochastic dependencies between flows due to resource sharing inside the network. However, by carefully utilizing the basic SNC concepts in the network analysis the necessity of taking these dependencies into account can be minimized. To that end, we unleash the power of the pay multiplexing only once principle (PMOO, known from the deterministic network calculus) in the SNC analysis. We choose an analytic combinatorics presentation of the results in order to ease complex calculations. In tree-reducible networks, a subclass of general feedforward networks, we obtain an effective analysis in terms of avoiding the need to take internal flow dependencies into account. In a comprehensive numerical evaluation, we demonstrate how this unleashed PMOO analysis can reduce the known gap between simulations and SNC calculations significantly, and how it favourably compares to state-of-the art SNC calculations in terms of accuracy and computational effort. Motivated by these promising results, we also consider general feedforward networks, when some flow dependencies have to be taken into account. To that end, the unleashed PMOO analysis is extended to the partially dependent case and a case study of a canonical example topology, known as the diamond network, is provided, again displaying favourable results over the state of the art.

Analysis of Saturation in the Emergency Department: A Data-Driven Queuing Model Using Machine Learning.

Emergency department is a key component of the health system where the management of crowding situations is crucial to the well-being of patients. This study proposes a new machine learning methodology and a queuing network model to measure and optimize crowding through a congestion indicator, which indicates a real-time level saturation.

Passenger congestion alleviation in large hub airport ground-access system based on queueing theory

Airport public transport systems are plagued by passenger queue congestion, imposing a substandard travel experience and unexpected delays. To address this issue, this paper proposes a bi-level programming for optimizing queueing network in airport access. Firstly, we derive queueing network for airport public transport system, which include the taxi, bus, and subway. Then, we propose a bi-level programming model for optimizing queueing network. The lower level subprogram is designed to solve the passenger transport mode choice, while the upper level subprogram is designed to minimize the number of passengers waiting to be served with queue tolls. Finally, we develop the successive weighted averages (MSWA) method to solve the lower subprogram's passenger share rates and the ant lion optimization (ALO) method to solve the bi-level program's queue toll scheme. The simulation results highlight that our strategy can alleviate queue congestion for daytime and evening scenarios and effectively improve evacuation efficiency.

A survey on TCP enhancements using P4-programmable devices

The increasing performance requirements of today’s Internet applications demand a reliable mechanism to transfer data. Many applications rely on the Transmission Control Protocol (TCP) as the transport protocol, due to its ability to adapt to properties of the network and to be robust in the face of many kinds of failures. However, improving the performance of applications that rely on TCP has been limited by the closed nature of legacy switches, which do not provide accurate visibility of network events. With the emergence of P4-programmable devices, developers can rapidly implement and test customized solutions that use fine-grained telemetry, provide sub round-trip time feedback to end devices to enhance congestion control, precisely isolate traffic to offer better Quality of Service (QoS), quickly detect congestion and re-route traffic via alternate paths, and optimize server resources by offloading protocols.This paper first surveys recent works on P4-programmable devices, focusing on schemes aimed at enhancing TCP performance. It provides a taxonomy classifying the aspects that impact TCP’s behavior, such as congestion control, Active Queue Management (AQM) algorithms, TCP offloading, and network measurement schemes. Then, it compares the P4-based solutions, and contrasts those solutions with legacy implementations. Lastly, the paper presents challenges and future trends.

A traffic responsive control framework for signalized junctions based on hybrid traffic flow representation

The paper proposes a traffic responsive control framework based on a Model Predictive Control (MPC) approach. The framework focuses on a centralized method, which can simultaneously compute the network decision variables (i.e., the green timings at each junction and the offset of the traffic light plans of the network). Furthermore, the framework is based on a hybrid traffic flow model operating as a prediction model and plant model in the control procedure. The hybrid traffic flow model combines two sub-models: an aggregate model (i.e., the Cell Transmission Model; CTM) and a disaggregate model (i.e., the Cellular Automata model; CA), using a transition cell to connect them. The whole framework is tested on a signalized arterial, performing several analyses to calibrate the MPC strategy and evaluate the traffic control approach using fixed and adaptive control strategies. All analyses are made in terms of total time spent, network total delay, queue lengths and degree of saturation.

Efficient instance reuse approach for service function chain placement in mobile edge computing

The combination of mobile edge computing and network function virtualization has led to the emergence of Virtualized Network Function (VNF) in a broader range of application scenarios. These latency-sensitive and highly dynamic services can be provided by combining multiple VNFs into Service Function Chains (SFCs). However, existing work has conspicuously neglected that online placing SFC with instance reuse can significantly improve resource utilization and save initialization time, which requires considering both the dynamic distribution of required VNFs over time and resource constraints on the edge network. In this paper, we initiate the study of Online SFC placement combined with Instance Reuse. An OSIR algorithm is proposed to gain a tradeoff between service costs and users’ quality of experience. The OSIR is designed based on deep reinforcement learning, which improves the system performance by maximizing the long-term cumulative reward. In OSIR, an SFC queue network is designed to extract the dynamic distribution of required VNFs over time, composed of memory space and the long short-term memory learning approach. The experimental results with real-world data traces show that OSIR can efficiently and effectively improve system performance and outperform the best result of all existing algorithms ranging from 17% to 26%.

On-demand valet charging for electric vehicles: Economic equilibrium, infrastructure planning and regulatory incentives

Many city residents cannot install their private electric vehicle (EV) chargers due to the lack of dedicated parking spaces or insufficient grid capacity. This presents a significant barrier towards large-scale EV adoption. To address this concern, this paper considers a novel business model, on-demand valet charging, that unlocks the potential of under-utilized public charging infrastructure to promise higher EV penetration. In the proposed model, a platform recruits a fleet of couriers that shuttle between customers and public charging stations to provide on-demand valet charging services to EV owners at an affordable price. Couriers are dispatched to pick up low-battery EVs from customers, deliver the EVs to charging stations, plug them in, and then return the fully-charged EVs to customers. To depict the proposed business model, we develop a queuing network to represent the stochastic matching dynamics, and further formulate an economic equilibrium model to capture the incentives of couriers, customers as well as the platform. These models are used to examine how charging infrastructure planning and regulatory intervention will affect the market outcome. First, we find that the optimal charging station densities for distinct stakeholders are different: couriers prefer a lower density; the platform prefers a higher density; while the density in-between leads to the highest EV penetration as it balances the time traveling to and queuing at charging stations. Second, we evaluate a regulatory policy that imposes a tax on the platform and invests the tax revenue in public charging infrastructure. Numerical results suggest that this regulation can suppress the platform’s market power associated with monopoly pricing, increase social welfare, and facilitate the market expansion.

An Analysis of a Stochastic ON-OFF Queueing Mobility Model for Software-Defined Vehicle Networks

We have recently witnessed a number of new software-defined paradigms of VANET in what is referred to as software-defined vehicle networks (SDVN). In order to evaluate the performance of these new proposals and architectures, analytical and simulation models are needed. In this paper, we propose an analytical model based on ON-OFF queueing networks under exponential and general service time distributions. The model can be used to evaluate the performance of SDVNs and takes into account the effect of mobility such as, hand overs, node turning ON/OFF, node going temporary out of coverage, and intermittent connections. This mobility effect was modelled as a queueing station with exponentially random ON-OFF service times, where traffic arrives according to a Poisson random process during the exponentially random ON period and the service time is exponentially distributed. However, during the OFF period the service time is exponentially distributed but with lower rates. We studied the ON-OFF queueing behaviour extensively for both finite-capacity and infinite-capacity queues. Three hypothetical SDVN scenarios were considered, taking into account the effect of mobility and the large number of connected nodes. Results were cross-validated with those obtained by a simulation model. These tools will be valuable for researchers interested in getting quantitative answers for their SDVN architectures.

Scheduling of Wireless Edge Networks for Feedback-Based Interactive Applications

Interactive applications with automated feedback will largely influence the design of future networked infrastructures. In such applications, status information about an environment of interest is captured and forwarded to a compute node, which analyzes the information and generates a feedback message. Timely processing and forwarding must ensure the feedback information to be still applicable; thus, the quality-of-service parameter for such applications is the end-to-end latency over the entire loop. By modelling the communication of a feedback loop as a two-hop network, we address the problem of allocating network resources in order to minimize the delay violation probability (DVP), i.e. the probability of the end-to-end latency exceeding a target value. We investigate the influence of the network queue states along the network path on the performance of semi-static and dynamic scheduling policies. The former determine the schedule prior to the transmission of the packet, while the latter benefit from feedback on the queue states as time evolves and reallocate time slots depending on the queue’s evolution. The performance of the proposed policies is evaluated for variations in several system parameters and comparison baselines. Results show that the proposed semi-static policy achieves close-to-optimal DVP and the dynamic policy outperforms the state-of-the-art algorithms.

Workstation layout strategies in Robotic Mobile Fulfillment Systems considering carbon emissions

A Robotic Mobile Fulfillment System (RMFS) in the e-commerce industry is an automated order picking system for reducing workers’ moving time, aiming to improve the efficiency of the warehouse. Robots are able to carry movable shelves, known as pods, traveling swiftly between the storage area and workstations, including pick and replenishment stations. This paper designs bidirectional robots driving rules and studies warehouse layout planning decision and evaluates system operational performance by modeling a Semi-Open Queueing Network (SOQN). Furthermore, we analyze the impact of different warehouse layout on system throughput time and carbon emission.

Analysis and Design of Rack-Climbing Robotic Storage and Retrieval Systems

Warehouses are becoming increasingly robotized. Autonomous rack-climbing robots have recently been introduced in e-commerce fulfillment centers. The robots not only retrieve loads from any level in a rack but also, roam the warehouse and bring the loads to order picking stations without using conveyors or lifts. This paper models and analyzes this system under both single and dual commands with different robot assignment (dedicated versus shared) and storage location assignment (class-based and random) policies. We study these policies in the presence of robot congestion. We evaluate the impact of two blocking protocols, a wait-outside-aisle policy and a block-and-recirculate policy, on the order throughput time. The system is modeled using semiopen queuing networks (SOQNs) for the different operating policies. The analytical models are validated using simulation. We also use this model to compare this system with a shuttle-based system. The results show that (1) the choice of the wait-outside-aisle policy or the block-and-recirculate policy mainly depends on the number of the robots in the system and the throughput requirement and that (2) the dedicated robot assignment policy can be an attractive policy, especially for a large system.

Stability and Optimization of Speculative Queueing Networks

We provide a queueing-theoretic framework for job replication schemes based on the principle “ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">replicate a job as soon as the system detects it as a straggler</i> ”. This is called job <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">speculation</i> . Recent works have analyzed replication on arrival, which we refer to as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">replication</i> . Replication is motivated by its implementation in Google’s BigTable. However, systems such as Apache Spark and Hadoop MapReduce implement speculative job execution. The performance and optimization of speculative job execution is not well understood. To this end, we propose a queueing network model for load balancing where each server can speculate on the execution time of a job. Specifically, each job is initially assigned to a single server by a frontend dispatcher. Then, when its execution begins, the server sets a timeout. If the job completes before the timeout, it leaves the network, otherwise the job is terminated and relaunched or resumed at another server where it will complete. We provide a necessary and sufficient condition for the stability of speculative queueing networks with heterogeneous servers, general job sizes and scheduling disciplines. We find that speculation can increase the stability region of the network when compared with standard load balancing models and replication schemes. We provide general conditions under which timeouts increase the size of the stability region and derive a formula for the optimal speculation time, i.e., the timeout that minimizes the load induced through speculation. We compare speculation with redundant- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula> and redundant-to-idle-queue- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula> rules under an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$S\&amp; X$ </tex-math></inline-formula> model. For light loaded systems, redundancy schemes provide better response times. However, for moderate to heavy loadings, redundancy schemes can lose capacity and have markedly worse response times when compared with the proposed speculative scheme.

Calibrating nonstationary queueing network models

Calibrating nonstationary queueing network models

Dynamic Vehicle Allocation Policies for Shared Autonomous Electric Fleets

In the future, vehicle sharing platforms for passenger transport will be unmanned, autonomous, and electric. These platforms must decide which vehicle should pick up which type of customer based on the vehicle’s battery level and customer’s travel distance. We design dynamic vehicle allocation policies for matching appropriate vehicles to customers using a Markov decision process model. To obtain the model parameters, we first model the system as a semi-open queuing network (SOQN) with multiple synchronization stations. At these stations, customers with varied battery demands are matched with semi-shared vehicles that hold sufficient remaining battery levels. If a vehicle’s battery level drops below a threshold, it is routed probabilistically to a nearby charging station for charging. We solve the analytical model of the SOQN and obtain approximate system performance measures, which are validated using simulation. With inputs from the SOQN model, the Markov decision process minimizes both customer waiting cost and lost demand and finds a good heuristic vehicle allocation policy. The experiments show that the heuristic policy is near optimal in small-scale networks and outperforms benchmark policies in large-scale realistic scenarios. An interesting finding is that reserving idle vehicles to wait for future short-distance customer arrivals can be beneficial even when long-distance customers are waiting.

RL-QN: A Reinforcement Learning Framework for Optimal Control of Queueing Systems

With the rapid advance of information technology, network systems have become increasingly complex and hence the underlying system dynamics are often unknown or difficult to characterize. Finding a good network control policy is of significant importance to achieve desirable network performance (e.g., high throughput or low delay). In this work, we consider using model-based reinforcement learning (RL) to learn the optimal control policy for queueing networks so that the average job delay (or equivalently the average queue backlog) is minimized. Traditional approaches in RL, however, cannot handle the unbounded state spaces of the network control problem. To overcome this difficulty, we propose a new algorithm, called RL for Queueing Networks (RL-QN), which applies model-based RL methods over a finite subset of the state space while applying a known stabilizing policy for the rest of the states. We establish that the average queue backlog under RL-QN with an appropriately constructed subset can be arbitrarily close to the optimal result. We evaluate RL-QN in dynamic server allocation, routing, and switching problems. Simulation results show that RL-QN minimizes the average queue backlog effectively.

A quantitative microbial risk assessment for touchscreen user interfaces using an asymmetric transfer gradient transmission mode.

The ubiquitous use of public touchscreen user interfaces for commercial applications has created a credible risk for fomite-mediated disease transmission. This paper presents results from a stochastic simulation designed to assess this risk. The model incorporates a queueing network to simulate people flow and touchscreen interactions. It also describes an updated model for microbial transmission using an asymmetric gradient transfer assumption that incorporates literature reviewed empirical data concerning touch-transfer efficiency between fingers and surfaces. In addition to natural decay/die-off, pathogens are removed from the system by simulated cleaning / disinfection and personal-touching rates (e.g. face, dermal, hair and clothing). The dose response is implemented with an exponential moving average filter to model the temporal dynamics of exposure. Public touchscreens were shown to pose a considerable infection risk (∼3%) using plausible default simulation parameters. Sensitivity of key model parameters, including the rate of surface disinfection is examined and discussed. A distinctive and important advancement of this simulation was its ability to distinguish between infection risk from a primary contaminated source and that due to the re-deposition of pathogens onto secondary, initially uncontaminated touchscreens from sequential use. The simulator is easily configurable and readily adapted to more general fomite-mediated transmission modelling and may provide a valuable framework for future research.

Improving the Mean-Field Fluid Model of Processor Sharing Queueing Networks for Dynamic Performance Models in Cloud Computing

Resource management in cloud computing is a difficult problem, as one needs to balance between adequate service to clients and cost minimization in a dynamic environment of interconnected components. To make correct decisions in such an environment, good performance models are necessary. A common modeling methodology is to use networks of queues, but as these are prohibitively expensive to evaluate for many applications, approximation methods for key metrics are frequently employed. One such method-that provides both transient solutions and short, scalable computation times-is the fluid model, which approximates the dynamics of the mean queue lengths using a system of ordinary differential equations. However, finding a fluid model that can adequately approximate an arbitrary queueing network is in general difficult. In the paper, we extend the state of the art with the following three contributions. First, we show that for any mixed multiclass queueing network of processor sharing and delay queues with phase-type service time distributions, such a fluid model can be found via the meanfield approximation. Furthermore, we propose an improved model based on smoothing of the processor share function that improves the performance of certain systems. Finally, using the smoothed mean-field model, we introduce an accurate closed-form approximation of the response time CDF over any subset of classes and queues.

Facilitating Load-Dependent Queueing Analysis Through Factorization (Extended Abstract)

We construct novel exact and approximate solutions for meanvalue analysis and probabilistic evaluation of closed queueing network models with limited load-dependent (LLD) nodes. In this setting, load-dependent functions are assumed to become constant after a finite queue-length threshold. For single-class models, we provide an explicit formula for the normalizing constant that applies to models with arbitrary LLD functions, whilst retaining constant complexity with respect to the total population size. From this result, we then derive corresponding closed-form solutions for the multiclass case and show that these yield a novel mean value analysis approach for LLD models. Significantly, this allows us to determine exactly the correction factor between a load-independent solution and a limited load-dependent one, enabling the reuse of state-of-the-art methods for loadindependent models in the analysis of load-dependent networks.

Queueing Network Controls via Deep Reinforcement Learning

Novel advanced policy gradient (APG) methods, such as trust region policy optimization and proximal policy optimization (PPO), have become the dominant reinforcement learning algorithms because of their ease of implementation and good practical performance. A conventional setup for notoriously difficult queueing network control problems is a Markov decision problem (MDP) that has three features: infinite state space, unbounded costs, and long-run average cost objective. We extend the theoretical framework of these APG methods for such MDP problems. The resulting PPO algorithm is tested on a parallel-server system and large-size multiclass queueing networks. The algorithm consistently generates control policies that outperform state-of-art heuristics in literature in a variety of load conditions from light to heavy traffic. These policies are demonstrated to be near optimal when the optimal policy can be computed. A key to the successes of our PPO algorithm is the use of three variance reduction techniques in estimating the relative value function via sampling. First, we use a discounted relative value function as an approximation of the relative value function. Second, we propose regenerative simulation to estimate the discounted relative value function. Finally, we incorporate the approximating martingale-process method into the regenerative estimator.

On the asymptotic optimality of the cμ-rule in queueing networks

Although the cμ-rule is proven to be exactly or asymptotically optimal in various parallel queueing networks, its performance in non-parallel queueing networks is relatively unexplored. We study the performance of the cμ-rule (that is, the performance of implementing the cμ-rule at all servers) in non-parallel queueing networks. We numerically show that the cμ-rule can perform poorly even in a simple tandem queue with two job types. We derive conditions under which the cμ-rule is asymptotically optimal in diffusion scale.